Accurate measurement of mechanical strain forces on railroad wheels has long been desirable. Knowledge of those strains helps analyze wheel strength, placement, derailment and other track conditions.
Wheel strain measurement has occasionally been made with devices mounted on the track itself. However, such wayside measurement is not continuous. Devices are mounted, and measurements taken, only every so many feet.
For continuous strain measurement, some type of measuring device must be mounted to the vehicle itself. Various wheel-mounted sensor designs have been attempted.
All wheel-mounted sensor designs share a need to cleanly isolate the perpendicular forces contributing to the strain force acting on a wheel. A wheel is subject to strain force composed of vertical, longitudinal (in direction of track) and lateral (side to side of wheel) forces.
An appropriate wheelset coordinate system for describing the dynamics of wheel loads is illustrated in FIG. 1. In FIG. 1 vertical, lateral, and longitudinal forces or loads are represented as V, L and T respectively. The rotational position of the wheel is defined as .THETA., while the lateral position of the wheel/rail contact point is defined as P.
Isolating the orthogonal V, L and T forces in a wheel-mounted sensor design is not easy. Measuring devices trying to measure one force component often pick up signals (crosstalk) from one or the other of the directions. The exact force components impinging on the wheel from each direction can therefore be hard to identify.
Attempts to solve the crosstalk problem have been made. British Rail for instance has employed a spoked-wheel strain sensor to separate load forces. Individual spokes measure individual force components. Despite a reduction in crosstalk, the spoked-wheel design is expensive, and suffers from lower sensitivity.
Other approaches have been attempted. Deutsche Bundesbahn (DB) has mounted strain sensors on the wheel axle, rather than the wheel itself. The strain force on the wheel is derived from the axle forces actually measured. This design is relatively inexpensive, but is not sensitive to the lateral position of the contact point (P) between the wheel and the rail. A number of other parties (including the Electro-Motive Division of GM Corporation) have attempted to apply strain sensors directly to the wheelplate itself, in a variety of configurations. Hybrid axle, wheelplate and bearing designs have also been contrived.
However, wheelplate-mounted sensor designs have, among other things, still encountered difficulties with cleanly isolating the component forces. More particularly, a wheelplate wired with a typical Wheatstone bridge as a measuring strain sensor produces a (voltage) sensor output of the form:
Equation 1 EQU E=f(.THETA.,P)V+g(.THETA.,P)L+h(.THETA.,P)T
This output relation assumes a homogeneous, isotropic and linearly elastic wheelplate. The "f", "g" and "h" functions represent the wheelplate sensitivity to the component vertical, lateral and longitudinal forces. Those force sensitivities can be conveniently represented by Fourier coefficients. Breaking the Fourier coefficients into equations for each perpendicular direction, a Fourier coefficient matrix of the form:
Equation 2 EQU .SIGMA..sub.i.sup.4 =1E.sub.i.sup.2 =.zeta..sub.V V.sup.2 +.eta..sub.V L.sup.2 +.xi..sub.V T.sup.2 +.kappa..sub.V VL EQU .SIGMA..sub.j.sup.2 =1E.sub.j.sup.2 =.zeta..sub.L V.sup.2 +.eta..sub.L L.sup.2 +.xi..sub.L T.sup.2 +.kappa..sub.L VL EQU .SIGMA..sub.k.sup.4 =1E.sub.k.sup.2 =.zeta..sub.p V.sup.2 +.eta..sub.p L.sup.2 +.xi..sub.p T.sup.2 +.kappa..sub.p VL
can be used to represent the wheel.
As noted, in strain sensor designs to present, isolating individual force components out of the output shown in Equations 1 and 2 has been difficult, because of crosstalk and other problems. Designs have attempted to isolate force components by methods such as placing the strain sensors in special areas of the wheelplate, and adjusting measuring circuits to dampen crosstalk. If the wheelplate sensitivity is represented in a matrix of Fourier coefficients, the special area may sought by trying to drive the non-diagonal coefficients to zero.
But "zeroing out" the matrix of Fourier coefficients is hard to achieve with precision. Practice has shown that this can only be accomplished with sensors mounted at very limited portions of the wheel, and at only a single contact position (P). This unduly restricts the sensor certain placement, and is not an effective or general solution.
As seen in Equation 2 the inventors have shown that it is not necessary to eliminate the non-diagonal elements of the coefficient matrix. The only requirement for obtaining a valid solution to the system of equations is that the coefficient matrix remain well conditioned for all loads and contact geometries. That is to say, the three equations depicted in Equation 2 must be linearly independent for all loads and contact geometries.